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103
Concept Maps as Hypermedia Components
, 1995
"... Concept mapping has a history of use in many disciplines as a formal or semiformal diagramming technique. Concept maps have an abstract structure as typed hypergraphs, and computer support for concept mapping can associate visual attributes with node types to provide an attractive and consistent ap ..."
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Cited by 48 (11 self)
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Concept mapping has a history of use in many disciplines as a formal or semiformal diagramming technique. Concept maps have an abstract structure as typed hypergraphs, and computer support for concept mapping can associate visual attributes with node types to provide an attractive and consistent appearance. Computer support can also provide interactive interfaces allowing arbitrary actions to be associated with nodes such as hypermedia links to other maps and documents. This article describes a general concept mapping system that is open architecture for integration with other systems, scriptable to support arbitrary interactions and computations, and cutomizable to emulate many styles of map. The system supports collaborative development of concept maps across local area and wide area networks, and integrates with WorldWide Web in both client helper and server gateway roles. A number of applications are illustrated ranging through education, artificial intelligence, active documents...
Spider diagrams: A diagrammatic reasoning system
 Journal of Visual Languages and Computing
, 2001
"... Spider diagrams combine and extend Venn diagrams and Euler circles to express constraints on sets and their relationships with other sets. These diagrams can be used in conjunction with objectoriented modelling notations such as the Unified Modeling Language. This paper summarises the main syntax a ..."
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Cited by 38 (11 self)
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Spider diagrams combine and extend Venn diagrams and Euler circles to express constraints on sets and their relationships with other sets. These diagrams can be used in conjunction with objectoriented modelling notations such as the Unified Modeling Language. This paper summarises the main syntax and semantics of spider diagrams. It also introduces inference rules for reasoning with spider diagrams and a rule for combining spider diagrams. This system is shown to be sound but not complete. Disjunctive diagrams are considered as one way of enriching the system to allow combination of diagrams so that no semantic information is lost. The relationship of this system of spider diagrams to other similar systems, which are known to be sound and complete, is explored briefly.
On Automating Diagrammatic Proofs of Arithmetic Arguments
 Journal of Logic, Language and Information
, 1999
"... . Theorems in automated theorem proving are usually proved by formal logical proofs. However, there is a subset of problems which humans can prove by the use of geometric operations on diagrams, so called diagrammatic proofs. Insight is often more clearly perceived in these proofs than in the corres ..."
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Cited by 31 (8 self)
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. Theorems in automated theorem proving are usually proved by formal logical proofs. However, there is a subset of problems which humans can prove by the use of geometric operations on diagrams, so called diagrammatic proofs. Insight is often more clearly perceived in these proofs than in the corresponding algebraic proofs; they capture an intuitive notion of truthfulness that humans find easy to see and understand. We are investigating and automating such diagrammatic reasoning about mathematical theorems. Concrete, rather than general diagrams are used to prove particular concrete instances of the universally quantified theorem. The diagrammatic proof is captured by the use of geometric operations on the diagram. These operations are the "inference steps" of the proof. An abstracted schematic proof of the universally quantified theorem is induced from these proof instances. The constructive !rule provides the mathematical basis for this step from schematic proofs to theoremhood. In ...
Effective Diagrammatic Communication: Syntactic, Semantic and Pragmatic Issues
 Journal of Visual Languages and Computing
, 1999
"... The study of systems of communication may be divided into three parts: syntax, semantics and pragmatics. Accounts of the embedding of textbased languages in the computational processes of reasoners and communicators are relatively well developed; with accounts available for a spectrum of languages ..."
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Cited by 25 (4 self)
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The study of systems of communication may be divided into three parts: syntax, semantics and pragmatics. Accounts of the embedding of textbased languages in the computational processes of reasoners and communicators are relatively well developed; with accounts available for a spectrum of languages which ranges from the highly formalised and constrained, such as formal logics, to the highly informal and unconstrained natural languages used in everyday conversations. Analogies between diagrams and such textual representations of information are quite revealing about both similarities and differences and can provide a useful starting point for exploring the issues in a theory of diagrammatic communication. This paper sketches out a theory of diagrammatic communication, based upon recent studies of the syntactic, semantic and pragmatic component issues which such a theory must accommodate. In the context of this theory an exploration is made of the issues involved in answering...
Abstract syntax and semantics of visual languages
 JOURNAL OF VISUAL LANGUAGES AND COMPUTING
, 1998
"... The effective use of visual languages requires a precise understanding of their meaning. Moreover, it is impossible to prove properties of visual languages like soundness of transformation rules or correctness results without having a formal language definition. Although this sounds obvious, it is s ..."
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Cited by 25 (9 self)
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The effective use of visual languages requires a precise understanding of their meaning. Moreover, it is impossible to prove properties of visual languages like soundness of transformation rules or correctness results without having a formal language definition. Although this sounds obvious, it is surprising that only little work has been done about the semantics of visual languages, and even worse, there is no general framework available for the semantics specification of different visual languages. We present such a framework that is based on a rather general notion of abstract visual syntax. This framework allows a logical as well as a denotational approach to visual semantics, and it facilitates the formal reasoning about visual languages syntax and semantics for the visual languages VEX, Show and Tell, and Euler Circles. We demonstrate the semantics in action by proving a rule for visual reasoning with Euler Circles and by showing the correctness of a Show and Tell program.
On the Completeness and Expressiveness of Spider Diagram Systems
 PROC. DIAGRAMS 2000, EDINBURGH, SEPT 2000. LNAI 1889
, 2000
"... Spider diagram systems provide a visual language that extends the popular and intuitive Venn diagrams and Euler circles. Designed to complement objectoriented modelling notations in the specification of large software systems they can be used to reason diagrammatically about sets, their cardinalit ..."
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Cited by 17 (7 self)
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Spider diagram systems provide a visual language that extends the popular and intuitive Venn diagrams and Euler circles. Designed to complement objectoriented modelling notations in the specification of large software systems they can be used to reason diagrammatically about sets, their cardinalities and their relationships with other sets. A set of reasoning rules for a spider diagram system is shown to be sound and complete. We discuss the extension of this result to diagrammatically richer notations and also consider their expressiveness. Finally, we show that for a rich enough system we can diagrammatically express the negation of any diagram.
Reasoning with Extended VennPeirce Diagrammatic Systems
, 2001
"... Traditionally the dominant formalist school in mathematics has considered diagrams as merely heuristic tools. However, the last few years have seen a renewed interest in visualisation in mathematics and, in particular, in diagrammatic reasoning. This has resulted from the increasing capabilities of ..."
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Cited by 14 (0 self)
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Traditionally the dominant formalist school in mathematics has considered diagrams as merely heuristic tools. However, the last few years have seen a renewed interest in visualisation in mathematics and, in particular, in diagrammatic reasoning. This has resulted from the increasing capabilities of modern computers, the key role that design and modelling notations play in the development process of software systems, and the emergence of the first formal diagrammatic systems. Constraint diagrams are a diagrammatic notation for expressing constraints that can be used in conjunction with the Unified Modelling Language (UML) in objectoriented modelling. Recently, full formal semantics and sound and complete inference rules have been developed for VennPeirce diagrams and Euler circles. Spider diagrams emerged from work on constraint diagrams. They combine and extend VennPeirce diagrams and Euler circles to express constraints on sets and their relationships with other sets. The spider diagram system SD1 developed in this thesis extends the second VennPeirce system that Shin investigated, Venn II, to give lower bounds for the cardinality of the sets represented
Aligning logical and psychological perspectives on Diagrammatic Reasoning
 Artificial Intelligence Review
, 1999
"... We advance a theoretical framework... ..."
Properties of Euler diagrams
 IN PROCEEDINGS OF LAYOUT OF SOFTWARE ENGINEERING DIAGRAMS
, 2007
"... Euler diagrams have numerous application areas, with a large variety of languages based on them. In relation to software engineering, such areas encompass modelling and specification including from a formal perspective. In all of these application areas, it is desirable to provide tools to layout Eu ..."
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Cited by 12 (10 self)
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Euler diagrams have numerous application areas, with a large variety of languages based on them. In relation to software engineering, such areas encompass modelling and specification including from a formal perspective. In all of these application areas, it is desirable to provide tools to layout Euler diagrams, ideally in a nice way. Various notions of ‘niceness ’ can be correlated with certain properties that an Euler diagram may or may not possess. Indeed, the relevant layout algorithms developed to date produce Euler diagrams that have certain sets of properties, sometimes called wellformedness conditions. However, there is not a commonly agreed definition of an Euler diagram and the properties imposed on them are rarely stated precisely. In this paper, we provide a very general definition of an Euler diagram, which can be constrained in varying ways in order to match the variety of definitions that exist in the literature. Indeed, the constraints imposed correspond to properties that the diagrams may possess. A contribution of this paper is to provide formal definitions of these properties and we discuss when these properties may be desirable. Our definition of an Euler diagram and the formalization of these properties provides a general language for the Euler diagram community to utilize. A consequence of using a common language will be better integration of, and more accessible, research results.
Visual language theory: Towards a Human computer interaction perspective
 IN
, 1998
"... The main reason for using visual languages is that they are often far more convenient to the user than traditional textual languages. Therefore, visual languages intended for use by both computers and humans ought to be designed and analyzed not only from the perspective of computational resource re ..."
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Cited by 12 (0 self)
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The main reason for using visual languages is that they are often far more convenient to the user than traditional textual languages. Therefore, visual languages intended for use by both computers and humans ought to be designed and analyzed not only from the perspective of computational resource requirements, but equally importantly, also from the perspective of languages that are cognitively usable and useful. Theoretical and practical research on visual languages need to take into account the full context of a coupled humancomputer system in which the visual language facilitates interactions between the computational and the cognitive parts. This implies that theoretical analyses ought to address issues of comprehension, reasoning and interaction in the cognitive realm as well as issues of visual program parsing, execution and feedback in the computational realm. The human aspect is crucial to visual languages, and therefore we advocate a correspondingly broadened scope of inquiry for visual language research. In this chapter we describe aspects of human use of visual languages that ought to be important considerations in visual language research and design, and summarize research from related fields such as software visualization and diagrammatic reasoning that addresses these issues. A framework consistent with the broadened scope of visual language research is proposed and used to categorize and discuss several formalizations and implemented systems. In the course of showing how a sample of current work fits into this framework, open issues and fruitful directions for future research are also identified.